In projection exposure apparatuses, in particular with a projection objective having a high numerical aperture (e.g., a numerical aperture of greater than 1.3), targeted forming of the polarization state both in the illumination device and in the projection objective is often desirable for the purpose of obtaining high resolutions. In this case, in the illumination device and also in the projection objective, a polarization state initially set can be influenced by various effects in an undesirable manner. The effects include, for example, a stress birefringence present in the lens material (e.g., due to mount-induced forces, compaction, and/or thermal effects), polarization-induced birefringence, a birefringence present in antireflective or highly reflective layers on the optical components (e.g., due to form birefringence or due to different Fresnel reflection and transmission for orthogonal polarization states), and/or an intrinsic birefringence of the lens material.